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I would like to work with the dividend-adjusted Black Scholes formula and need to estimate the dividend yield and risk-free rate. I know that I could compute both rates exogenously. But I am working with the S&P 500 index as underlying asset, so it is more difficult to obtain the dividend yield, as it consists of up to 500 individual dividend payments.

That's why I would like to use Futures prices to the expectations of future dividend payments. The risk-free rate minus the dividend yield is calculated as: $$ r_{t, \tau} - d_{t, \tau} = \frac{ln(F_{t, \tau}/S_t)}{\tau} $$ Unfortunately, I only have Futures contracts that expire every 3 months: March, June, September and December.

My question: Is there a way to approximate the dividend yield/risk-free rate for the two months in between (April, May, July, August, ...) from the given Futures prices?

Thanks in advance!

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